Machine Learning in Databases

Hash Tables, B-Trees, and Learned Indexes

Tyler Elliot Bettilyon

Teb for short.

 

I used to work at some startups that don't matter.

 

I teach programming and computer science.

 

I write about technology and its impact on the world.

 

Tyler Elliot Bettilyon

Website:   www.tebslab.com

Medium:  @tebbaVonMathenstien

Twitter:    @TebbaVonMaths

What Is This Talk About?

Database Indexing

  • You have a lot of data to store.
     
  • You need to look up specific items quickly.
     
  • We use an index for this.

What Is This Talk About?

Well Known Indexing Strategies

  • Hash tables
     
  • B-Trees

What Is This Talk About?

New Research Into "Learned Indexes"

  • Google + MIT Collaboration
     
  • https://www.arxiv.com/papers/1712.01208/

What Is This Talk About?

How Do Learned Indexes Stack Up?

  • When do the old-school algorithms have an advantage?
     
  • When do learned indexes have an advantage?
     
  • What are the trade-offs at play?

What Is Indexing?

Indexing helps us quickly find specific items within a large collection of data.

 

Especially helpful when that data is not sorted by the field you're querying against.

What Is Indexing?

id:        0

name: Teb

age:     79

...

This is a single row in a database table

These are all rows in the same table

What Is Indexing?

Where is Tim?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

What Is Indexing?

Finding Tim Without an Index...

X

?

?

?

?

?

?

?

?

?

?

Are you Tim?

X

X

X

X

What Is Indexing?

Finding Tim With an Index

Tim

The Index

Where is Tim?

Offset 7

What Is Indexing?

Indexing is a trade off between memory usage and computation speed.

 

The index occupies memory, but it makes queries faster.

Performance of Indexes

5 major performance considerations:

 

  1. Type of query (individual vs range)
     
  2. Lookup speed
     
  3. Cost of inserting a new record
     
  4. Cost of deleting a record
     
  5. Total size & utilization rate

Performance of Indexes

Type of Query
 

Where is Tim?

Fetch everyone age 5-12.

Performance of Indexes

Lookup Speed

The Index

Where is Tim?

Offset 7

How long does this take?

Performance of Indexes

Cost to insert

id:        99

name: Yannet

age:     30

...

The Index

How long does it take to update the index?

Performance of Indexes

Cost to delete

The Index

How long does it take to update the index?

Performance of Indexes

Size & utilization

The Index

How much additional data is this index?

What is the information density of this index?

Performance of Indexes

A Caveat

Indexing is primarily a tool used when there is a lot of data.

 

Optimizing for the number of hard drive accesses is more common than optimizing for total operations

Hash Tables

Hash Function

Arbitrary Data

Integer

Hash functions map arbitrary data to an integer, deterministically.

Hash Tables

Hash Table

Hash Function

Arbitrary Data

Integer

Hash table indexes map those integers to memory locations of database records

Memory Address

Hash Tables

Hash Function

"Tim"

15

The Hash Table:

The Database Table:

Hash Tables

  • Great for individual lookups, poor for range queries.
     
  • Query time is O(1)  — access the index once then access memory once.
     
  • Insertion and deletion are O(1) — access the index once.
     
  • Size & Utilization varies based on the choice of hash function and collision handling strategy — it's common for hash tables to have ~50% utilization.

Performance

Hash Tables

  • Collision handling strategy can make a huge difference (Linear probing vs chaining vs cuckoo hashing).
     
  • Inserts might require the whole index to be rebuilt if there are too many collisions, or the table runs out of space, which also impacts utilization.
     
  • Hash function choice can impact rate of collisions and speed to compute, which can impact speed and utilization.

Gotchas

B-Trees

The structure of a B-Tree represents sorted data, similar to a Binary Search Tree.

...

First

Last

...

B-Trees

The root node and each internal node are lists of pointers to sorted sections of the overall data.

a b-d e-g
h-l j-p q-t
u-v w-x y-z
aa-ab ac-ad ae-ag
ah-al aj-ap aq-at
au-av aw-ax ay-az
aeon afar
afraid agriculture

Root

Internal

Leaf

B-Trees

Leaf nodes contain the items themselves and a pointer to their values location in the database

a b-d e-g
h-l j-p q-t
u-v w-x y-z
aa-ab ab-ad ae-ag
ah-al aj-ap aq-at
au-av aw-ax ay-az
aeon afar
afraid agriculture

Root

Internal

Leaf

B-Trees

Because indexes are optimized for hard drive access, the size of each node is often based on hard drive block size.

...

First

Last

...

Root

2. Iterate over block

Hard Drive/Secondary Storage

3. Indicates which block to read next

1. Read block to RAM

B-Trees

  • Great for range queries, and still pretty good for individual queries.
     
  • Query time is O(log n)  — leaf nodes contain the actual data we need and the tree depth is log n.
     
  • Insertion and deletion are O(log n) — same as querying.
     
  • Size & Utilization varies based on the size of each node, overall balance of the tree, and how full each node is.

Performance

B-Trees

  • B-Trees must be relatively balanced or performance won't be O(log n).
     
  • Inserting into an already full node can result in that node being "split" into two — Costs extra computation plus both nodes will be at low  (~50%) utilization.
     
  • Deleting a node might require an expensive rebalancing operation.

Gotchas

Learned Indexes

A Google + MIT Collaboration explored the idea of applying machine learning to indexing

https://arxiv.org/abs/1712.01208

Learned Indexes

"Hash Tables and B-Trees are just models"

Index

Item of Interest

Location in Memory

This is essentially regression!

Learned Indexes

"Range indexes are just CDFs"

estimatedPosition = Model(key) ∗ numberOfElements

Learned Indexes

One important caveat...

ML Model

Item of Interest

Approximate Location in Memory

Indexes must return the exact location in memory — there is no room for any error.

Learned Indexes

This is addressed by storing the min and max error over the dataset.

ML Model

Item of Interest

Approximate Location in Memory

Lookups don't have as strong theoretical guarantees, but are bounded by magnitude of maxError - minError

Min Error

Max Error

Learned Indexes

ML Model

Item of Interest

Approximate Location in Memory

Min Error

Max Error

Min Error + Guess

Max Error + Guess

Guess

Learned Indexes

Models could also replace hash functions.

Hash Function

Arbitrary Data

Integer

ML

Model

Arbitrary Data

Integer

Hash Table

Learned Indexes

The researchers used a collection of simpler models, not a single large model.

This helped with last mile accuracy.

Lessons Learned

The researchers focused on simple models. The paper is a proof of concept.

  • Researchers focused on small fully connected neural nets.

     
  • Focused on create once, read only, in memory, data structures.

     
  • Write heavy workloads are a huge problem for these models, and this paper doesn't even try to address that.

Lessons Learned

Promising size and speed savings!

B-trees compared to learned indexes

Lessons Learned

Promising utilization improvements, slower speeds

Learned hash functions compared to standard hash function

Models are better at taking the distribution into account

  • B-Trees and Hash Tables are agnostic of the data's distribution, which negatively impacts utilization.
     
  • ML Models inherently take the distribution of the data into account, which can help with utilization rates.

Lessons Learned

Lessons Learned

Overfitting is kind of the goal.

  • Indexes never have to predict the location of data that hasn't yet been indexed.
     
  • Accurate 'predictions' for data in the index is much more important than generalizing to held out data.

Average Error is less important than error bounds

Min Error + Guess

Max Error + Guess

Guess

Lessons Learned

Interesting properties at scale

  • Standard indexes grow as the input data grows.
     
  • An ML Model's size may not have to scale up as data grows, it only needs  sufficient complexity to produce N values as output.

Lessons Learned

Takes advantage of new hardware

  • Moore's Law is dead or dying and classical index structures are not well suited to parallelization.
     
  • ML workloads are a main driver of current hardware advancements — meaning learned indexes are better positioned to take advantage of new hardware

Lessons Learned

Multidimensional indexing

  • Classical index structures only take into account one feature of some data.
     
  • Learned index structures could index across multiple dimensions, allowing a wide variety of queries and filters to be applied at once.
     
  • This is because of ML's strength in identifying high dimensional relationships

Lessons Learned

Thanks For Coming

My name is still Tyler Elliot Bettilyon

Website:   www.tebslab.com

Medium:  @tebbaVonMathenstien

Twitter:    @TebbaVonMaths

Thanks For Coming

My name is still Tyler Elliot Bettilyon

I'm teaching a deep learning course focused on computer vision starting Tuesday the 28th.

 

https://learn.xnextcon.com/

Learned Indexes

By tebba-von-mathenstein

Learned Indexes

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